Cauchy problem for dissipative Hölder solutions to the incompressible Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations on the 3-dimensional torus which are continuous or Hölder continuous for any exponent $θ<\frac{1}{16}$. Using the techniques introduced in \cite{DS12} and \cite{DS12H}, we prove the existence of infinitely many (Hölder) continuous initial vector fields starting from which there exist infinitely many (Hölder) continuous solutions with preassigned total kinetic energy.

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